Chemical Physics Letters 577 (2013) 92–95
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Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Formation of linear Ni nanochains inside carbon nanotubes: Prediction
from density functional theory
Jurijs Kazerovskis a,⇑, Sergei Piskunov a, Yuri F. Zhukovskii a, Pavel N. D’yachkov b, Stefano Bellucci c
a
Institute for Solid State Physics, University of Latvia, 8 Kengaraga Str., Riga LV-1063, Latvia
Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow 119991, Russia
c
INFN-Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044 Frascati, RM, Italy
b
a r t i c l e
i n f o
Article history:
Received 21 February 2013
In final form 22 May 2013
Available online 29 May 2013
a b s t r a c t
First principles calculations have been performed to investigate the ground state properties of monoperiodic single-walled carbon nanotubes (CNTs) containing nanochain of aligned Ni atoms inside. Using the
PBE exchange-correlation functional (Exc ) within the framework of density functional theory (DFT) we
predict the clusterization of Ni filaments in (n,0) CNTs for n P 9 and for (n; n) CNTs for n P 6. The variations in formation energies obtained for equilibrium defective nanostructures allow us to predict the
most stable Ni@CNT compositions. Finally, the electronic charge redistribution has been calculated in
order to explore intermolecular properties leading to stronger Ni–Ni bond formation.
Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction
Carbon nanotubes with encapsulated monoatomic nanochains
of magnetic metals (e.g., Ni) are technologically important onedimensional (1D) Me@CNT nanostructures fabricated and studied
in recent years [1]. Their mechanical, physical and chemical properties can be applied in various nanodevices as well as magnetic
data storage and drug delivery platforms. In addition, the CNT
walls can provide an effective barrier against oxidation and, thus,
ensure long-term stability of the encapsulated metals. Nevertheless, the nanotubes filled with magnetic metals do not always display designed properties because the amount and location of
magnetic particles inside the tubes are difficult to be controlled.
To guide reliable fabrication of Me@CNT, it is important to understand the formation mechanism of metal nanochains or separated
nanoparticles in nanotubes. In this study, we consider monoatomic
chains of nickel atoms encapsulated into single-walled (SW) CNTs
of armchair-type ðn; nÞ; n ¼ 3; 4; 5; 6; 7, and zigzag-type ðn; 0Þ; n ¼
7; 8; 9; 10; 11, chiralities. We determine the optimal size of CNT
for encapsulating a single monoatomic chain, the most stable configuration of Ni atoms adopted by nanochain and its influence on
CNT’s electronic structure. Recently, a number of both experimental [2–4] and theoretical [5–7] studies of transition metal nanofilaments encapsulated into CNTs of different morphologies were
reported. However, we are not aware in any systematic study devoted to monoatomic Ni nanofilament encapsulated inside CNT.
⇑ Corresponding author.
E-mail address: [email protected] (J. Kazerovskis).
0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.cplett.2013.05.046
The first principles method employed for this study allow us to
describe 1D nanotubes in their original space form, unlike the standard Plane-Wave (PW) methods, which are quite widespread nowadays for ab initio calculations on low-dimensional periodic
systems, including carbon nanotubes [8,9]. Indeed, to restore the
3D periodicity in the PW NT calculations, the x y supercell of
nanotubes is artificially introduced: the NTs are placed into a
square array with the intertube distance equal to 2–3 nm. At such
separations the NT–NT interaction is found to be rather small;
however, the convergence of results obtained in such calculations
depends on the artificial intertube interactions demanding additional computational efforts to ensure their negligibility. The method that allows CNT formation starting from hexagonal graphite
bulk and (0001) monolayer, in accordance with a model of structural transformation (3D ? 2D ? 1D), is described elsewhere
[10]. Using this approach we have constructed the monoperiodic
unit cells for ideal carbon nanotubes of armchair (n ¼ 3; 4; 5; 6; 7)
and zig-zag (n ¼ 7; 8; 9; 10; 11) types of CNT chiralities. Monoatomic Ni nanochain has been then incorporated into these nanotubes
being fixed along the CNT axis (Figure 1). Off–center displacement
of the incorporated Ni filament has been restricted by imposed
rototranslational symmetry (rotation axis of nth order). The coordinates of all atoms in each of studied Ni@CNT nanostructures have
been optimized along symmetry-preserved directions. The imposed symmetry sufficiently reduces the computational efforts,
however, it limits to some extent the flexibility of applied model.
On the other hand, the CNTs under study have diameters less then
9 Å and, thus, the chosen model is very well consistent with recent
HRTEM observation of Mo monoatomic nanochains in doublewalled CNTs with inner diameter between 6 and 8 Å [2]. Within
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J. Kazerovskis et al. / Chemical Physics Letters 577 (2013) 92–95
grals ITOL3, as well as pseudo-overlap tolerances for exchange
integral series, ITOL4 and ITOL5) [11] have been set to 8, 8, 8, 8,
and 16, respectively. (If the overlap between the two atomic orbitals is smaller than 10ITOLn , the corresponding integral is truncated.) Further increasing of k-mesh and threshold parameters
results in much more expensive calculations yielding only a
negligible gain in the total energy (107 a.u.). Calculations are
considered as converged when the total energy obtained in the
self-consistent field procedure differs by less than 107 a.u. in
two successive cycles. Effective charges on atoms as well as net
bond populations have been calculated according to the Mulliken
population analysis.
The formation energies of a Ni filament inside CNTs have been
estimated as follows:
Ef ¼
Fig. 1. Schematic representation of selected equilibrium structures of Ni filament
inside (a) CNT (3,3), (b) CNT (7,7), (c) CNT (7,0), and (e) CNT (10,0) as calculated by
means of PBE Exc within the DFT-LCAO formalism. Gray balls stand for carbons, blue
(dark gray) ones for nickels. (For interpretation of the references to colour in this
figure caption, the reader is referred to the web version of this article.)
the framework of our model, increased unit cell of both armchair
and zig-zag CNTs contains 5 Ni atoms.
1 tot
tot
ðE
Etot
Ni ECNT Þ;
N Ni@CNT
ð1Þ
where N is the number of atoms in the unit cell, Etot
Ni@CNT is the calculated total energy of CNT containing Ni filament, Etot
Ni is the total energy calculated for the Ni filament in the vacuum, and Etot
CNT stands
for the total energy calculated for the perfect CNT. In our simulations, the coordinates of all atoms in studied nanostructures have
been allowed to relax. Such an optimization procedure allows one
to obtain the equilibrium geometries by calculating the local minima on the potential energy surface (PES), and, thus, to predict reliable formation energies. We are aware that in order to confirm the
phase stability of studied nanostructures the frequency calculations
are necessary to exclude the presence of the optical mode having
imaginary frequency. Test calculations performed on armchair-type
Ni@CNT nanostructures do not reveal the imaginary frequency
modes, giving us a ground to assume that the PES local minima calculated for other nanostructures under study are the real minima
not the saddle points.
3. Results and discussion
2. Computational details
In this study, we have performed the first principles simulations
on Ni@CNTs using formalism of the localized Gaussian-type functions (GTFs), which form the basis set (BS), and exploiting periodic
rototranslation symmetry for efficient ground-state calculations as
implemented in ab initio code CRYSTAL developing formalism of
localized atomic orbitals (LCAO) for calculations on periodic systems [11]. Due to precise reproduction of electronic properties of
both Ni bulk and surface [12] as well as single- and double-wall
CNTs [13], the GGA–DFT scheme based on the non-local Perdew–
Burke–Erzernhof (PBE) Hamiltonian [14] has been used for the
band structure calculations. For Ni, the all-electron BS has been
adopted in the form of 8s-64111sp-41d, with the exponents of core
and valence shells being unchanged. In addition, the two virtual Ni
sp-functions with exponents 0.63 and 0.13, respectively, and
d-function with the exponent 0.38 have been used as optimized
in bulk calculations (see Ref. [12] for more details). All-electron
BS for C has been adopted in the form of 6s-311sp-11d [11]. Recently, these C and Ni BSs were used by us for the DFT-LCAO simulation of CNT growth upon the nanostructured Ni substrate [15].
To provide the balanced summation over the direct and reciprocal lattices, the reciprocal space integration has been performed by
sampling the Brillouin zone (BZ) with the 10 1 1 Pack–Monkhorst k-mesh [16] that results in 6 homogeneously distributed kpoints at the segment of irreducible BZ. The threshold parameters
of CRYSTAL code (ITOLn) for evaluation of different types of bielectronic integrals (overlap and penetration tolerances for Coulomb
integrals, ITOL1 and ITOL2, overlap tolerance for exchange inte-
Table 1 lists the Ni@CNTs formation energies calculated according to Eq. 1. Formation energy mainly depends on the diameter of
the nanotube, and is practically independent of its chirality. The
smallest nanotubes that were found to be able to encapsulate a
Ni nanochain have been the (3,3) and the (7,0) with diameters of
4.32 and 5.67 Å, respectively. Smaller nanotubes are deformed
noticeably upon Ni insertion and lose their structure becoming
unstable. The larger nanotubes studied here are (7,7) and (11,0)
with diameters of 9.59 and 8.70 Å, respectively. For nanotubes of
Table 1
Equilibrium diameter of Ni@CNTs (D in Å), energy of nanostructure formation (Ef in
eV/atom, see Eq. 1), distance between the nearest-neighbor Ni atoms in the nickel
nanofilament encapsulated into CNT (dNiNi in Å), difference in Ni–Ni distance in
encapsulated filament with respect to filament placed in the vacuum (SNiNi in %), Ni–
Ni bond populations (PNiNi in milli e), Ni–C bond populations (PNiC in milli e), and
magnetic moment on Ni atoms (M Ni in Bohr magnetons) as calculated by means of the
PBE-DFT method.
Ni@CNT (3,3)
Ni@CNT (4,4)
Ni@CNT (5,5)
Ni@CNT (6,6)
Ni@CNT (7,7)
Ni@CNT (7,0)
Ni@CNT (8,0)
Ni@CNT (9,0)
Ni@CNT (10,0)
Ni@CNT (11,0)
Ni (vacuum)
Ni (bulk)
D
Ef
dNiNi
SNiNi
P NiNi
P NiC
M Ni
4.32
5.56
6.88
8.22
9.59
5.62
6.38
7.15
7.92
8.70
0.21
0.17
0.13
0.10
0.08
0.16
0.14
0.12
0.10
0.09
2.49
2.46
2.46
2.18
2.18
2.49
2.36
2.16
2.13
2.13
2.25
2.50
10.8
9.5
9.3
3.1
3.1
10.4
4.9
4.0
5.2
5.5
0
11.1
142
414
472
652
664
400
544
630
676
684
600
174
78
28
16
4
0
60
28
12
6
2
0.32
1.09
1.12
1.27
1.25
1.13
1.32
1.27
1.26
1.21
1.21
0.62
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J. Kazerovskis et al. / Chemical Physics Letters 577 (2013) 92–95
Fig. 2. 2D difference electron density plots DqðrÞ (the sum of total electron densities in the Ni@CNT minus the sum of these densities in the Ni nanochain and perfect
nanotube projected onto the section planes across CNT containing Ni filament as shown in Figure 1): (a) Ni@CNT (5,5) front view, (b) Ni@CNT (5,5) side view, (c) Ni@CNT
(10,0) front view, (d) Ni@CNT (10,0) side view. Dash-dot (black) isolines correspond to the zero level. Solid (red) and dashed (blue) isolines describe positive and negative
values of the difference in electron density, respectively. Isodensity curves are drawn from 0.01 to +0.01 eÅ3 with an increment of 0.0001 eÅ3. (For interpretation of the
references to colour in this figure caption, the reader is referred to the web version of this article.)
Fig. 3. Equilibrium structures of Ni filament encapsulated inside CNT (10,0) with
doubled unit cell (10 Ni atoms inside). Gray balls stand for carbons, blue (dark gray)
ones for nickels. (For interpretation of the references to colour in this figure caption,
the reader is referred to the web version of this article.)
larger diameter, the bonding between the Ni nanochain and the
nanotube slowly disappears and the formation energy increases
asymptotically toward a constant value, due to the bonding between Ni atoms. Formation energies of Ni@CNTs have been found
decreasing along with decreasing the nanotube diameter due to
weakening of Ni–C bond. This leads to the stronger Ni–Ni bonding
and formation of linear Ni nanoclusters inside CNTs of diameter
more than 7 Å. Such a tendency is confirmed by a difference charge
density maps shown in Figure 2 and the calculated Mulliken bond
populations (Table 1). The difference in stability of the Ni nanochain inside CNTs of armchair and zigzag chiralities with the sim-
Fig. 4. Total and projected density of states (PDOS) of Ni@CNT (5,5) (a) and Ni@CNT (10,0) (b). Zero at the energy scale corresponds to the Fermi level. Positive PDOS stands for
spin-up electrons, negative for spin-down electrons.
J. Kazerovskis et al. / Chemical Physics Letters 577 (2013) 92–95
ilar diameter is caused by a larger mismatch between their initial
periodicities in the zz-CNT and the Ni nanochain (cf. 9.6% and
14.0% for ac- and zz-chiralities, respectively).
In order to precise the structure of decomposed Ni nanochain
inside CNT, we have performed geometry optimization of doubled
unit cell of Ni@CNT (10,0) containing 10 Ni atoms inside. As a result of such calculations, we obtain the formation of linear 6-nickel
nanoclusters (Figure 3). This gives us a ground to conclude that the
tendency of the Ni nanofilament fragmentation inside CNT does
not depend on the unit cell length. Note that according to our modeling, the formation of linear Ni nanoclusters is predicted for
Ni@CNTs up to diameter of 9.6 Å, where the Ni–C bond is very
weak, but does not disappears completely. For CNTs of larger diameter, the formation of different Ni nanoclusters may be expected.
The calculated projected densities of states (PDOSs) are shown
in Figure 4. The Ni filament in vacuum in its ferromagnetic ground
state is metallic with a magnetic moment of 1.21 vs. 0.62 lB in the
Ni bulk (Table 1). Main contributions to the DOS peak at the Fermi
level of the Ni nanochain in vacuum come from dxz and dyz orbitals,
while contributions from dx2 y2 orbitals, forming EF level of Ni bulk,
remain mainly unchanged. Ni filament encapsulation inside CNT
leads to hybridization of Ni 3d and C 2sp orbitals. This hybridization is stronger pronounced in CNTs of smaller diameter (Figure 4a)
than in Ni@CNT nanostructures of larger diameter (Figure 4b).
Since Ni filament is initially a metallic structure, its encapsulation
inside CNTs makes them metallic, even if the pristine CNT is semiconducting. For instance, one can observe the conducting state of
Ni at zig-zag CNT (10,0) (Figure 4b) with the pseudo-gap of carbon
sp states shifted 0.5 eV below the Fermi level. All studied Ni@CNT
nanostructures are stabilized in ferromagnetic ground state. Similar to the Ni nanochain in vacuum, the magnetic moment of Ni
nanofilament inside CNT is practically doubled with respect to Ni
bulk (Table 1).
4. Summary and conclusions
Summing up, we have performed large-scale first-principles
calculations on a carbon nanotube with encapsulated monoatomic
chain. Nanofilament encapsulation inside CNTs with diameter less
then 6 Å has been found energetically more favorable, due to stronger interatomic Ni–C bonding, while weakening of Ni–C bond of
Ni@CNTs with diameter larger than 6 Å yields an additional freedom for formation of stronger Ni–Ni bonds leading to clusterization of Ni nanofilament. In all the cases, monoatomic Ni
nanochain preserves a ferromagnetic ground state with magnetic
95
moment on Ni as twice as larger than in the Ni bulk (0.62 lB ). Enhanced magnetic properties arise mainly from geometry-dependent unfilled d band and sp–d hybridization effects typical for
transition metal nanofilaments encapsulated inside nanotube [5].
CNTs containing monoatomic Ni nanochain exhibit metallic behavior, even if pristine nanotube is semiconductor (i.e., (n,0) CNTs).
Therefore, encapsulation of Ni nanofilament in CNTs is a way to
create the highly conductive 1D hybrid nanostructures suitable
as interconnects for future nanoelectronic circuits.
Acknowledgements
The research leading to these results has received support from
the EC’s Seventh Framework Program under Grant agreement Nr.
247007 (CACOMEL). The authors are thankful to R.A. Evarestov
and S.A. Maksimenko for stimulating discussions.
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